EUROPT 2025
Abstract Submission

407. An unconstrained method for nonconvex Pareto front approximation

Invited abstract in session WB-10: Global Multi-Objective Optimization, stream Multiobjective and Vector Optimization.

Wednesday, 10:30-12:30
Room: B100/8011

Authors (first author is the speaker)

1. Ina Lammel
Optimization, Fraunhofer ITWM
2. Karl-Heinz Küfer
Optimization, Fraunhofer ITWM

Abstract

In multi-objective optimization, approximating a Pareto front is a common task to help a decision-maker understand his or her options. Most scalarization-based approximation schemes for nonconvex Pareto fronts use constraints on the feasible set to guide the next solution to be computed to a particular region of the Pareto front.
However, many powerful specialized solvers cannot handle constraints.
We propose a new algorithm for the approximation of nonconvex Pareto fronts that only solves unconstrained optimization problems if the underlying multi-objective optimization problem is unconstrained.
The algorithm uses a utility function-based scalarization method that incorporates penalty functions to approximate constraints. We show the completeness of the approach, i.e. every Pareto point can be the solution of a scalarization problem.
The approximation algorithm is based on approximated boxes. We provide conditions under which a solution computed with approximated constraints actually fulfills the constraints and discuss the implications for the approximation algorithm and the use of domination cones to bound trade-offs.
We illustrate the performance of the algorithm with numerical and practical examples and compare it to a box-based algorithm that uses a Pascoletti-Serafini scalarization approach.

Keywords

Status: accepted

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